GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Aug 2018, 07:50

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A sequence of non-zero real numbers is such that every term after the

Author Message
TAGS:

### Hide Tags

DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1342
Location: India
A sequence of non-zero real numbers is such that every term after the  [#permalink]

### Show Tags

09 Jun 2018, 11:17
00:00

Difficulty:

55% (hard)

Question Stats:

68% (01:37) correct 32% (01:42) wrong based on 28 sessions

### HideShow timer Statistics

A sequence of non-zero real numbers is such that every term after the first term, is half of its previous term. What is the fifth term of this sequence?

(1) Product of fourth and sixth terms of this sequence is twice the fifth term.

(2) Sum of third and fourth terms of this sequence is six times the fifth term.
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 505
WE: Supply Chain Management (Energy and Utilities)
A sequence of non-zero real numbers is such that every term after the  [#permalink]

### Show Tags

09 Jun 2018, 12:44
amanvermagmat wrote:
A sequence of non-zero real numbers is such that every term after the first term, is half of its previous term. What is the fifth term of this sequence?

(1) Product of fourth and sixth terms of this sequence is twice the fifth term.

(2) Sum of third and fourth terms of this sequence is six times the fifth term.

Let the non-zero real numbers are $$a_1, a_2,.......,a_{n-1},a_n$$.
Given:- $$a_n=\frac{a_{n-1}}{2}$$ or$$a_{n-1}=2a_n,$$ n>1
Question stem:- $$a_5=?$$

statement1,

Given,$$a_4*a_6=2a_5$$
Or, $$2a_5*\frac{a_5}{2}=2a_5$$
Or, $$a_5=2$$ (since the terms in the sequence are non-zero real numbers)
So, sufficient.

statement2, Given,$$a_3+a_4=6a_5$$
Or,$$2a_4+2a_5=6a_5$$
Or,$$a_4=2a_5$$,
Or, $$a_5$$=$$\frac{a_4}{2}$$ ;this is nothing but the re-statement of the data given in the question.
Hence, insufficient.

Ans. A
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1897
Re: A sequence of non-zero real numbers is such that every term after the  [#permalink]

### Show Tags

12 Jun 2018, 23:02

Solution

Given:
• In a sequence of non-zero real numbers, every term after first term is half of its previous term

To find:
• The fifth term of the sequence

Analysing Statement 1

• As per the information given in statement 1, product of fourth and sixth terms is twice the fifth term

If we assume fourth term to be 4x, then fifth term will be 2x and sixth term will be x
As per the statement,
• 4x * x = 2 * 2x
Or, $$4x^2 = 4x$$
Or, x = 1 (as x is non-zero)

Therefore, we can find the value of the fifth term

Hence, statement 1 is sufficient to answer

Analysing Statement 2

• As per the information given in statement 2, sum of third and fourth terms is six times the fifth term

If we assume the third term to be 4y, then fourth term will be 2y and fifth term will be y
As per the statement,
• 4y + 2y = 6 * y
Or, 6y = 6y

We don’t get any solution from this equation

Hence, statement 2 is not sufficient to answer

Hence, the correct answer is option A.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: A sequence of non-zero real numbers is such that every term after the &nbs [#permalink] 12 Jun 2018, 23:02
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.